Method of cutting single crystals

ABSTRACT

A method of dividing single crystals, particularly of plates of parts thereof, is proposed, which can comprise: pre-adjusting the crystallographic cleavage plane ( 2′ ) relative to the cleavage device, setting a tensional intensity (K) by means of tensional fields ( 3′, 4′ ), determining an energy release rate G(α) in dependence from a possible deflection angle (α) from the cleavage plane ( 2′ ) upon crack propagation, controlling the tensional fields ( 3′, 4′ ) such that the crack further propagates in the single crystal, wherein G(0)≧2γ e (0) and simultaneously at least one of the following conditions is satisfied: 
     
       
         
           
             
               
                 
                   
                     
                       
                          
                         
                           
                             ∂ 
                             G 
                           
                           
                             ∂ 
                             α 
                           
                         
                          
                       
                       
                         α 
                         = 
                         0 
                       
                     
                     ≤ 
                     
                       2 
                       ⁢ 
                       
                         
                           β 
                           e 
                         
                         h 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       if 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             ∂ 
                             2 
                           
                           ⁢ 
                           G 
                         
                         
                           ∂ 
                           
                             α 
                             2 
                           
                         
                       
                     
                     ≤ 
                     0 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   or 
                 
               
               
                 
                   ( 
                   2.1 
                   ) 
                 
               
             
             
               
                 
                   
                      
                     
                       
                         ∂ 
                         G 
                       
                       
                         ∂ 
                         α 
                       
                     
                      
                   
                   ≤ 
                   
                     2 
                     ⁢ 
                     
                       
                         β 
                         e 
                       
                       h 
                     
                     ⁢ 
                     
                       ∀ 
                       
                         
                           α 
                           ⁢ 
                           
                             : 
                           
                           ⁢ 
                           
                             α 
                             1 
                           
                         
                         &lt; 
                         α 
                         &lt; 
                         
                           
                             α 
                             2 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2.2 
                   )

CROSS REFERENCE AND PRIORITY

This application claims the benefit of U.S. Provisional Application60/996,396, filed Nov. 15, 2007, entitled “Verfahren zum Trennen vonEinkristallen”, which is hereby incorporated by reference in itsentirety. This application further claims the benefit of GermanApplication No. 10 2007 056 115.8, filed Nov. 15, 2007, entitled“Verfahren zum Trennen von Einkristallen”, which is hereby incorporatedby reference in its entirety.

FIELD OF THE INVENTION

The invention relates to a method of separating single crystals, e.g.,single crystalline plates or wafers or parts thereof. In particular, theapplication relates to a method of dividing single crystals including acrack propagation that is self-adjusting.

TECHNICAL BACKGROUND

Single crystalline wafers comprising semiconducting materials are usedas substrates for the manufacturing of micro-electronic components suchas field effect or hetero-bipolar transistors, and of opto-electroniccomponents, such as laser or luminescence diodes. By means of distinctprocesses such as CVD, MOCVD, LPE, MBE the functional layers aredeposited and optionally reworked upon those substrates, or aregenerated within the substrate by means of ion implantation. Thesesubstrates then run through complex structuring processes undergoingmultiple applications of exposure masks.

For the purpose of orientation (adjustment) of the exposure masks andoptionally for the necessary distinction between a front face and a rearface of the substrate, the substrate comprises a so-called orientationflat (OF) and an identification flat (IF), which is offset with regardto the orientation flat by 90° in the clockwise or counter-clockwisedirection. The wafer normal and the surface normal of the flats aregenerally perpendicular with respect to each other. Conventionalmanufacturing processes of wafers having flats include the generation ofthe flats by means of grinding. The adjustment accuracy of theorientation flats with regard to the crystallographic <110>-directionmay amount to ±1°, for the identification flat ±5°, in case of aconventional wafer manufacturing, but values even up to ±0.02° may beachieved for the orientation flat employing the above method. Flatsmanufactured by grinding may comprise mis-orientations fluctuating alongthe flats as well as chips at the edges, which affect the function ofthe flats as references for the adjustment of exposure masks. This isparticularly valid in the case of manufacturing laser diodes, whichnecessitate high precision and further undisturbed, sharp-edged flatshaving an adjustment accuracy of ≦|0.02°| over a length relevant for therespective technology.

It is well-known that the orientation accuracy of the flats can beincreased, if these are generated by cleaving the generally brittlesemiconductor materials instead of grinding the flats, thereby employingnatural cleavage planes. For example, in the case of III-Vsemiconductors, the {110}-planes are natural cleavage planes. From U.S.Pat. Nos. 5,279,077 and 5,439,723 there are known wafers provided withflats generated by such cleaving accordingly. From U.S. Pat. No.5,154,333 there is known a cleaving device, which is used to carry outcleavage with a predefined bending stress of a wafer, which contains aseed crack generated by scribing the wafer. However, a disadvantage ofthe mechanical cleaving device arises in that the crack progress can notbe controlled, and in that due to the initialization of the breakage bymeans of a seed break at the wafer edge a complex fracture mode isrealized.

Alternatively there are thermal dividing methods, which deal with acombination of local heating and neighboring local cooling. A basicmethod relates to a process of cutting flat glass by means of thermallyinduced stress which is described in DE 28 13 302. According to thismethod glass is heated in one area and cooled in another area, bothareas being provided on the glass on at least one of its two main facesand being placed one after the other on the intended straight cuttingline, and further being sharply delineated and symmetric with respect tothe cutting line. Temperature gradients result in the glass along thethickness direction and in the direction of the scribe line. Thetemperature gradients cause thermal stress, which starting from theinitial crack at the edge drives a crack perpendicular to the main facesand along the predetermined straight cutting line. Therein the crackprogress velocity can be controlled by regulating the appliedtemperatures and the feeding of the heating and cooling device.

From WO 93/20015 there is known a method of dividing semiconductorcomponents. According to this method the formation of tensile strengthin a region between a heating laser beam and a subsequent coolinginitiates a breakage. Using this method, the shape, direction, depth andpropagation velocity as well as the accuracy of the breakage generatedby thermal stress shall be controlled.

One feature of known methods of dividing brittle materials bypropagating a crack is the generation or the presence of an initialcrack. In the vicinity of the tip of the crack a stress field isgenerated using a suitable method such as, e.g., the above mentionedmechanical bending stress, or by applying a thermal load. This stressfield leads to a complex load at the propagation front of the crack,which may be characterized by a stress-intensity factor K. If the stressfield is selected, such thatK>K_(C),  (1.1)wherein K_(C) is the critical stress-intensity factor specific for thematerial, the crack length increases until the conditionK≦K_(C)  (1.2)is fulfilled. K>K_(C) is the propagation condition of the separationprocess, which has to be maintained continually or in intervals, untilthe complete separation is achieved.

The crack propagation proceeds according to the principle of minimizingthe free energy of the body that is to be divided. This means, that thecrack propagates such that in isotropic materials themechanical-energy-release rate G becomes a maximum. In anisotropicmaterials a principle of minimizing the effective surface energy 2γ_(e)of the divided surfaces competes with the principle of maximizing therate of the mechanical energy release when minimizing the total energyof the system during the crack propagation.

$\begin{matrix}{\frac{\mathbb{d}U}{\mathbb{d}C} =  {{2\;\gamma_{e}} - G}arrow{Min} } & (1.3)\end{matrix}$wherein U denotes the total energy of the system, and C denotes thesurface area generated by means of crack propagation.

This means, that with regard to the above-mentioned methods thepropagation of the crack is controlled by the time and positiondependent stress fields in the case of isotropic materials. Ifcrystallographic cleavage planes are present, which are characterized bya minimum effective surface energy, the direction of crack propagationenforced by the tensional fields (G→max) competes with the directions ofthese crystallographic cleavage planes upon crack propagation. As aconsequence, employing the above-described methods one is restricted inpractice to produce only such cleavage planes, which comprise steps orleaps into neighboring lattice planes. This may exert disadvantageouseffects on technologically relevant cleavage surfaces such as resonatorsurfaces of laser components, or on accuracy of the orientation ofcleaved flats.

In theory the production of completely planar cleavage surfaces could beachieved where a planar tensile stress field perpendicular to a desiredcleavage plane is generated. In this case the stress fields and thecleavage plane would be coordinated with each other to such an extentthat these do not compete with each other. However, these conditions cannot be kept in practice. For example, it would have to be required inthe case of cleaving laser components, that the wafer must be orientedwith high precision with respect to the cleavage device, in order toachieve a sufficient quality of the cleavage plane at least over thelength of the laser component. Even with the smallest deviations of thewafer orientation with respect to the generated tensional fields, stepsformed on the cleavage plane will become inevitable.

SUMMARY OF THE INVENTION

It is an object of the invention, to provide a method of dividing singlecrystals, which avoids the above mentioned disadvantages and whichsecures exact cleavage planes over a full distance up to the completeseparation of the desired parts.

The object is solved by a method according to claim 1, or by a singlecrystal according to claims 13 or 14. Embodiments and aspects of theinvention are set forth in the dependent claims.

According to the invention, cleavage planes having accuracies in therange of ≦|0.02°|, |0.01°|, |0.005°| or even less than |0.001°|—asmeasured over the extent of the respective area relevant for thetechnology or a plurality of portions thereof—can possibly be obtained.The area relevant for the respective technology corresponds in the caseof laser diodes for example with a length of a laser resonator, or inthe case of integrated circuits with the edge length of a chip to beseparated. Upon separation of material in order to form flats itcorresponds to the flat length. Also, the manufacturing of a naturalcleavage plane along the crystallographic grid plane becomes possibledue to the self-adjusted cleaving proposed herein.

The orientation accuracy of a separation surface of the single crystalwith respect to a crystallographic grid plane is measured by aligningthe crystal with a reference face, wherein at least two points of theseparation surface abut on the reference face. Using an X-ray goniometerthe orientation of the crystallographic grid plane can then bedetermined with respect to this reference plane. The grid planeorientation is then related to the reference surface plane resulting inan angle difference, which herein represents the accuracy.

The orientation of the separation surface with respect to the referencesurface according to the method used for determining the grid planeorientation can also be obtained by following different approaches ascompared with the above described mechanical abutment, e.g., by applyingoptical methods.

Besides the determination of the global orientation differences of thecleavage surface obtained according to this method using a lengthrelevant for the present technology, a local orientation difference canalso be obtained by sub-dividing this technologically relevant surfacelength into portions of, e.g., 2 mm and performing the orientationmeasurement using for example an optical microscope, a miniatureinterferometer, a white light interferometer or an autocollimator. Theorientation accuracy then corresponds to the largest of these measuredlocal differences.

The cleavage planes that may be obtained according to certainembodiments of the present invention are distinguishable as such fromsurfaces of semiconductor plates having another orientation when knownmeasurement methods are applied such as the LEED method (low energyelectron diffraction), cf. Qian, G. X., Martin, R. M., Chadi, D. J., inPhys. Rev. B, Vol. 37, p. 1303. (1988), or Bechstedt, F. “Principles ofSurface Physics”, Springer Verlag, Berlin, ISBN 978-3-540-00635-0,Chapter 1.2.4; pages 16-18. Thereby it is taken advantage of the factthat natural cleavage planes of III-V-semiconductors show merely arelaxed, but no reconstructed arrangement of atoms near the surface,which latter is the case for other orientations.

The method has the advantage that the previous determination andadjustment of the crystallographic cleavage planes for the cleavagedevice are required only with common accuracies. The precise orientationof the propagating crack is facilitated by the process conditionsaccording to certain embodiments of the invention, which enforce aself-adjustment of the direction of crack propagation in precisely oneof the crystallographic cleavage planes without steps or jumps.

BRIEF DESCRIPTION OF THE DRAWINGS

Further advantages and effects become evident from the description of anembodiment taken in conjunction with the Figures. In the Figures:

FIG. 1 shows a schematical top view of a wafer to be cleaved;

FIG. 2 shows the mechanical-energy-release rate G and the effectivesurface energy 2γ_(e) upon compliance with a first condition;

FIG. 3 shows the mechanical-energy-release rate G and the effectivesurface energy 2γ_(e) upon compliance with a second condition;

FIG. 4 shows the mechanical-energy-release rate G and the effectivesurface energy 2γ_(e) upon compliance with a third condition;

FIG. 5 shows the mechanical-energy-release rate G and the effectivesurface energy 2γ_(e) upon compliance with a fourth condition;

FIG. 6 shows a first phase of crack propagation;

FIG. 7 shows a second phase of crack propagation, which is controlled bythe relative movement of the stress fields (e.g., in isotropicmaterials);

FIG. 8 shows a phase of crack propagation in the case of a deviationfrom the desired cleavage direction when a crystallographic cleavageplane is present and when the stress fields are asymmetrically adjustedwith respect to the cleavage plane;

FIG. 9 shows a phase of crack propagation in a desired cleavagedirection in the case of an ideal symmetrical adjustment of the stressfields with respect to the cleavage plane;

FIG. 10 shows a schematical representation of the orientation of aGaAs-wafer in the cleavage device;

FIG. 11 shows an example of the maximum error consisting of a deviationof the position and direction between the desired cleavage plane and themovement direction as well as the generated stress fields in the startregion;

FIG. 12 shows an example of the maximum error consisting of a deviationof the position and direction between the desired cleavage plane and themovement direction as well as the generated stress fields in the targetregion;

FIG. 13 shows the mechanical-energy-release rates G⁻ and G₊ in thestart- and target regions in dependence of angle α; and

FIG. 14 shows a phase of crack propagation under compliance with certainconditions.

DETAILED DESCRIPTION OF EMBODIMENTS

In the following the invention is described by means of an embodiment ofa cleaving process of a GaAs-Wafer by means of thermally induced stressfields. At first, the wafer is provided to the cleavage device. Theadjustment of the wafer with respect to the cleavage device is performedby virtue of a previously formed marking, e.g., a short flat, which bymeans of example is grinded and oriented by means of X-raydiffractometry. Thereby an accuracy of the flat orientation with respectto the {110}-cleavage plane of 0.1° can be achieved in practice.Similarly, other markings or short flats perpendicular or in apredetermined relation to the cleavage planes may be considered aspre-adjustment means. The pre-adjustment with respect to the movementdirection may be carried out with the help of stops or employing opticalmethods.

As becomes schematically evident from FIG. 1, an initial crack 2 isformed in a {110}-cleavage plane of the GaAs-wafer 1. Ideally, theinitial crack 2 is formed in a cleavage plane which is parallel to apreferred gliding direction of the α-dislocations.

The initial crack 2 is for example generated by an indenter with definedgeometry (Vickers, Knoop-indenter). Similarly, other geometries or ascoring of the surface are possible. By proper selection of theindentation load and geometry the formation of B-cracks perpendicularthereto can be avoided.

Due to thermally induced stress fields, a plane edge-crack extending tothe wafer backside is generated from the indentation-induced crack inthe {110}-cleavage plane. This edge-crack serves as a plane initialcrack for the further crack propagation, or for the desired cleavagedirection, or for the cleavage plane 2′, respectively. Herein, thethermally induced stress fields are dimensioned, such that the initialcrack can not yet propagate further in this phase.

Thereafter, a stress intensity K is generated for the purpose of crackpropagation, and the quantity G(α) is determined, which represents therate of energy release upon further crack propagation in dependence of adeflection of the crack from the cleavage plane about an angle α. Thecrack propagation may be regarded as a superposition of a twist (twistconfiguration) about the angle φ around an axis perpendicular to thecrack front of the initial crack and a rotation about an angle θ aroundan axis in the crack front of the initial crack (tilt configuration).Both cases can be considered separately. The described method accordingto the invention is valid for both cases, such that for furtherconsideration it is sufficient to refer to a deflection angle α(with α=θfor the tilt configuration and α=φ for the twist configuration). Theembodiment is detailed with regard to the example of thetilt-configuration without restricting the validity of the general case.The stress intensity K is generated by employing known methods such asfor example the method according to DE 28 13 302 or the method accordingto WO 93/20015. Therein, one or more heat sources 4 as well as one ormore heat sinks 3 (cf. FIGS. 11, 12, 14) are localized on one or bothwafer faces, such that ideal symmetrical stress fields are obtained withrespect to the wafer thickness as well as with respect to the desiredcleavage direction. The heat sources can be generated for example byabsorption of laser light, and the heat sinks can be generated by anapplication of cooling aerosols such as described for example in WO93/20015. Similarly, other variants are possible as well. The heatsources and heat sinks are controlled and positioned such that a crackpropagation is enabled. The temperature has to be sufficiently low inorder to avoid plastic deformations. For GaAs a temperature of less thanabout 300° C. is considered as being appropriate.

The dimensioning or control, or even a feedback control, of the stressfields is carried out, such that crack propagation occurs continually orin intervals, wherein crack propagation is characterized byG(0)≧2γ_(e)(0). According to certain embodiments of the invention thedimensioning or control of the stress fields is performed such that atleast one of the following conditions is satisfied:

$\begin{matrix}{{{{\frac{\partial G}{\partial\alpha}}_{\alpha = 0} \leq {2\frac{\beta_{e}}{h}\mspace{14mu}{if}\mspace{14mu}\frac{\partial^{2}G}{\partial\alpha^{2}}} \leq 0}{or}}\mspace{11mu}} & (2.1) \\{{\frac{\partial G}{\partial\alpha}} \leq {2\frac{\beta_{e}}{h}{\forall{{\alpha\text{:}\alpha_{1}} < \alpha < {\alpha_{2}.}}}}} & (2.2)\end{matrix}$

Herein, the symbols denote:

-   α possible deflection angle upon crack propagation from the cleavage    plane-   α₁, α₂ range of angles, in which the necessary condition for a crack    propagation (1.1) is satisfied-   G(α) mechanical-energy-release rate in dependence of a deflection of    the crack from the cleavage plane about angle α.-   γ_(e)(0) effective surface energy of cleavage surface-   γ_(e) effective surface energy depending on direction-   β_(e) effective step energy (material specific)-   h step height (material specific).

The effective free surface energy γ_(e), which is used in fracturemechanics, is determined in breakage experiments from a relation betweenfracture strength and crack length. This quantity further contains—ascompared with the intrinsic surface energy γ_(s)—energy portions ofdissipative processes. To these belong—among others—the formation ofdislocations in the process zone or plastic zone, the emission ofacoustic energy or the occurrence of dissipative structures (fracturestructures) at the fracture surfaces. Hence, the surface energy γ_(e) islarger than the intrinsic surface energy γ_(s).

For the specific free step energy the following approximation may befound regarding thermo-dynamic equilibrium:β_(e) =−nk _(B) T ln η(1+2η),η=exp(−ε/k _(B) T).

Therein n denotes the step density with n=1/a, k_(B) denotes theBoltzmann constant, ε denotes the binding energy between closestneighbours in the crystal lattice, and a denotes the distance betweenbuilding units within the step.

The binding energy ε can be estimated from the sublimation energyΔH_(sub)(T) of the crystal (“congruent vaporization”) and thecoordination number Z of the considered crystal:ε≈ΔH _(sub) /Z,wherein ΔH_(sub)(T) is obtained from a calculation of the thermo-dynamicequilibrium X_(s)

X_(g) with the thermo-dynamic data of the solid (s) and the gaseous (g)phase X.

The free step energy can also be determined experimentally.

For GaAs following values can be assumed:

The effective free surface energy of GaAs {110}-cleavage surfacesobtained from fracture experiments yields

γ_(e)(0)≈(0.86±0.15) J/m². By investigation of the vicinity of thecleavage front, it could be ensured that dissipative processes can beneglected, i.e., the measured effective free surface energy approximatesthe intrinsic surface energy

γ_(s)(0)≈0.82 J/m², the latter being deduced from crystal growth.

For GaAs {110}/<001>, i.e., <001> oriented steps on a {110}-cleavagesurface with a tilting axis parallel to the <001> vector, the stepenergy has been estimated with the following data:ΔH _(sub)(300 K)=451.4 kJ/mol,Z=4→ε≈1.17 eV;

-   -   and for T=300 K: η≈45.25.

The distance of atoms in a step parallel to the <001>-vector amounts toa₀=0.565325 nm, while the height of a double step amounts toh=a₀/√2=0.399 nm. As a result of the above formula, the free step energybecomes:β_(e)≈3.31·10⁻¹⁰ J/m, andβ_(e) /h≈0.83 J/m².

This value approximately agrees with the intrinsic free surface energyγ_(s)≈0.82 J/m² of a {110}-cleavage plane.

For the free step energy the same conclusions as for the surface energymay analogously be derived. The effective step energy experimentallyderived can be larger than the step energy estimated herein due todissipative portions. By indicating the theoretically obtained stepenergy, the right side in conditions (2.1) and (2.2) is known.

Stress fields can be calculated obeying the conditions of the heatsources and sinks by employing simulation calculations. But also directmeasurement of the stress is possible, for example via stressbirefringence, ultrasonic microscopy, micro-Raman-spectroscopy etc.Thereof, the mechanical-energy-release rate G is calculated for thepreset stress field in dependence from possible deflections of the crackabout angle α. By controlling and positioning the heat sources andsinks, the stress fields are adjusted, such that the above mentionedconditions are satisfied.

Thereby, an angular range α₁<α<α₂ exists, in which the conditionG≧2γ_(e) is satisfied. This range depends on the stress fields and thematerial characteristics as well as on the misorientation of theemployed cleavage device from the targeted cleavage plane. In theangular range between α₁ and α₂ the necessary condition (1.1) for thecrack propagation is satisfied. The control according to the certainembodiments of the invention, or the dimensioning of the stressintensity K aiming at a compliance with conditions (2.1) or (2.2)facilitates, that the crack is not deflected in the angular rangeα₁<α<α₂, rather it moves over the complete separation distance withinthe targeted cleavage plane.

The unavoidable mis-orientation of the cleavage device, i.e. a stressintensity K with mixed crack opening modes K_(I)+K_(II)+K_(III), causesa mechanical-energy-release rate G(α) which is unsymmetrical withrespect to the desired crack propagation direction in the cleavage planeα=0 in dependence from possible deflection angles α. Further, the crackpropagates in a direction, in which the quantity g=G−2γ_(e) becomesmaximum. The control or the dimensioning of the stress intensity Krespectively, aiming at a compliance with the conditions (2.1) or (2.2)guarantees, that even in the case of a mis-orientation of the cleavagedevice, or in case of a stress intensity K with mixed crack openingmodes K_(I)+K_(II)+K_(III), a maximum of the quantity g is alwaysobtained at α=0. Hence, the crack propagation is enforced in a desiredlattice plane by self-adjustment of the crack propagation direction. Asa result, the cleavage surfaces having a high orientation accuracy inthe range of at least ≦|0.01°|, ≦|0.005°| or even ≦|0.001°| can begenerated. Further, cleavage surfaces having a minimum step density,ideally without steps, can be produced within the completetechnologically relevant area (flats, resonator surfaces, etc.).

Two situations, in which the conditions according to certain embodimentsof the invention are satisfied, are illustrated in FIGS. 2 and 3.

FIG. 2 shows the energy release rate G and the effective surface energy2γ_(e) as well as g=G−2γ_(e) under compliance with the condition

${\frac{\partial G}{\partial\alpha}}_{\alpha = 0} \leq {2\frac{\beta_{e}}{h}\mspace{14mu}{and}\mspace{14mu}\frac{\partial^{2}G}{\partial\alpha^{2}}} \leq {0{\forall{{\alpha\text{:}\alpha_{1}} < \alpha < {\alpha_{2}.}}}}$

FIG. 3 shows the energy release rate G and the effective surface energy2γ_(e) as well as g=G−2γ_(e) under compliance with the condition

${\frac{\partial G}{\partial\alpha}} \leq {2\frac{\beta_{e}}{h}{\forall{{\alpha\text{:}\alpha_{1}} < \alpha < {\alpha_{2}.}}}}$

Using the method, surfaces such as for example flats having anorientation accuracy of 0.01°—as measured over the surface rangerelevant for this technology—can be applied to a wafer, i.e., anaccuracy commonly achieved in practice by a grinding process can beincreased by one order of magnitude. The method ensures that theadjustment accuracy between the movement direction and the cleavageplane of 0.1° is sufficient in order to constrain the crack propagationin the cleavage plane with an accuracy of ≦0.01°. First results showthat accuracies of even ≦0.005° or ≦0.001° may be obtained. Finally, acompletely stepless ideal cleavage surface can be obtained which extendsprecisely along the natural crystallographic plane.

FIGS. 4 and 5 show situations, in which the mis-orientation of thecleavage device, or a stress intensity K with mixed crack opening modesis present and the conditions according to certain embodiments of theinvention are not satisfied.

FIG. 4 illustrates the energy release rate G and the effective surfaceenergy 2γ_(e) as well as g=

${G - {2\;\gamma_{e}\mspace{14mu}{with}\mspace{14mu}{\frac{\partial G}{\partial\alpha}}_{\alpha = 0}}} > {2{\frac{\beta_{e}}{h}.}}$In FIG. 4 the crack propagation occurs at α=α_(f), i.e. the crackdeviates from the desired cleavage direction α=0. On the correspondinglygenerated surface, steps and curved surface areas are produced. Theorientation accuracy of the technologically relevant areas (flats,resonator surfaces) is not sufficient and of less quality than desired.

FIG. 5 shows the energy release rate G and the effective surface energy2γ_(e) as well as g=G−

${2\;\gamma_{e}\mspace{14mu}{with}\mspace{14mu}{\frac{\partial G}{\partial\alpha}}} > {2\frac{\beta_{e}}{h}\mspace{14mu}{for}\mspace{14mu}\alpha} > {\alpha_{g}.}$In FIG. 5 the crack propagation at α=0 is unstable. Upon exceeding theangle α≧α_(g) a deviation of the crack propagation from the desiredplane α=0 occurs.

FIGS. 6 to 9 show different cases of crack propagation in the wafer. Bycontrolling and positioning the heat sources and heat sinks, acompression stress maximum 4′ and a tensile stress maximum 3′ isgenerated. The heat sources and sinks are positioned such as to locatethe compression stress maximum 4′ in front of the crack tip 5 in thepropagation direction, and the tensile stress maximum 3′ behind thecrack tip 5, as shown in FIG. 6. Within the range between the tensilestress and compression stress maxima, the condition K=K_(C) or G=2γ_(e)is satisfied at time step t=t₀ at a predetermined position P(0). By arelative movement between the temperature fields and the wafer, which isshown in FIG. 7 by the arrow 6, the conditions (1.1) K>K_(C) orG>2γ_(e), or (1.2) K≦K_(C) or G≦2γ_(e) can be controlled. I.e., thecrack tip 5 can be advanced, stopped or further moved as desired. Therelative movement can be carried out by a movement of the heat sourcesand heat sinks (laser focus or cooling nozzles, respectively), or it canbe carried out by a movement of the wafer, or it can be carried out by acombination of both. Dissipative or dynamical effects can be avoided bycontrolling the propagation velocity. The propagation velocity can beselected to sufficiently small values, such that a quasi static crackpropagation at thermo-dynamic equilibrium can be assumed (v<<⅓ of thesound velocity). The crack propagation follows the relative movement 6between the stress fields and the wafer 1. This is utilized in priorart, in order to cut complicated geometries, which may be straight orcurved.

If crystallographic cleavage planes are present the influence of thecleavage planes competes with the influence of the stress fields 3′ and4′ during the relative movement 6 between the tensional fields and thewafer, as described above, or the cleavage direction 2′ competes withthe movement direction 6 of the device during the growth of the crack.The situation is depicted in FIG. 8. At an infinitesimal relativemovement 6 by d{right arrow over (r)}, the crack is generally deviateddue to the energy principle (1.3) by angle α_(f). This corresponds tothe situation shown in FIG. 4. The tip of the crack is located at theposition P(t₀+dt), where the condition G(α_(f))=2γ_(e)(α_(f)) isachieved after time t=t₀+dt (quasi static crack propagation). In thismanner undesired steps are generally created on the cleavage surfaces,or deviations from the desired cleavage direction occur.

In order to avoid the competition between the cleavage direction and thestress fields, maximum values of the tensile stress should—according toknown fracture mechanical principles—be directed perpendicularly to thedesired cleavage plane. In order to achieve this situationappropriately, an ideally symmetrical adjustment of the tensional fields4′ and 3′ (i.e., the heating source and sink) would have to be providedrelative to the cleavage plane. This adjustment also has to bemaintained during the complete separation process, i.e. over the fulldistance of the cross-section of the GaAs-wafers. This means that themovement direction 6 of the device has to be adjusted ideally parallelto the cleavage plane 2′ as well as to the symmetry line of thetensional fields. This situation is depicted in FIG. 9. After a relativemovement by d{right arrow over (r)} the crack tip remains at a positionP(t₀+dt) at which the condition G(0)=2γ_(e)(0) is reached after a timet=t₀+dt. This means that the crack fully extends within the cleavageplane. This ideal situation is, however, not achievable in practice.This would require the measurement and adjustment of the cleavage planewith respect to the heating sources and sinks as well as with respect tothe movement direction of the device with very high precision, which cannot be achieved from the viewpoint of present production techniques andeconomics. Using the certain embodiments of the invention, however, asurface is generated which is oriented with very high accuracy.

FIG. 10 shows the orientation of the GaAs-wafer 1 in the cleavagedevice. As described above, a marking or short flat 7 is commonlypresent, which is grinded with a predetermined orientation tolerancewith respect to the crystallographic directions. Thereby, underpractical circumstances and with justifiable efforts an accuracy of theflat orientation 8 with respect to the {110}-cleavage planes of 0.1° isachievable. The flat 7 is pre-adjusted with respect to the movementdirection 6 of the relative movement between the stress fields and thewafer. Applying the separation method according to certain embodimentsof the invention, a surface (flat) is formed on the wafer having anorientation accuracy of ≦|0.01°|. I.e., the accuracy, which in practicecan be achieved using a grinding process, has been increased by an orderof magnitude. The method according to certain embodiments of theinvention facilitates that the adjustment accuracy between the movementdirection 6 and the cleavage plane 2′ of 0.1° suffices to constrain thecrack propagation within the cleavage plane to an accuracy of at least±0.01°. This can be continued from a wafer edge 9 to an opposed waferedge 9, or there may be present a predetermined region 10, within whichthe requirements to orientation accuracy of the flat 11 to be generatedhave to be fulfilled. The size and geometry of this region 10 may varyand depends on different technological requirements. Accuracies of≦0.005°| or even ≦0.001°| are also possible as well as a preciselystepless cleaving along the crystallographic plane.

By simulation calculations carried in advance, the stress fields arecalculated, preferably with the selected conditions with regard to theheating sources and sinks. The simulation is carried out in the regionsat the preset start and target points of the dividing process. This canbe done for example at the edges of the technologically used region 10within areas 12 and 13. Therein, the initial crack 2 within the cleavageplane at the edge of the start area 12 is present according to the abovementioned methods, preferably outside of region 10. Also other positionsare possible. The proportions of FIG. 10 are not drawn to the scale andare shown exaggeratedly for illustration purposes. The hitherto knownmeasurement accuracies (for example in X-ray diffractometry), the knowntolerances with regard to grinding and the known positional accuraciesdetermine the maximum error upon pre-adjustment of the wafer. Forexample, it is possible to determine with the help of simple geometricalrelations the maximum error between position and direction of thedesired cleavage plane and the movement direction 6 and also relative tothe generated tensional fields 3′ and 4′ in the start and target areas12 and 13 of the separation process. FIG. 11 shows an example of themaximum error in the start area 12. FIG. 12 shows an example of themaximum error in the target area 13. Note that also mirrored positionsare possible.

Now, the mechanical-energy-release rate G can be calculated for the caseof infinitesimal crack propagation in dependence from possibledeflections about the angle α for the given stress fields in the startposition 12 of the crack tip 5 of the initial crack. The same can becalculated in the planned target area 13 under the assumption that thecrack has not left the cleavage plane 2′. As a result there arise twofunctions G⁻(α) and G₊(α), which are given by the known maximum error inthe start and target positions. The true function G(α) is not known, butrepresents a state between G⁻(α) and G₊(α). By dimensioning andpositioning the heating sources and sinks the stress fields arearranged, such that the conditions according to certain embodiments ofthe invention

$\begin{matrix}{{{\frac{\partial G}{\partial\alpha}}_{\alpha = 0} \leq {2\frac{\beta_{e}}{h}}}{and}} & ( {3.1.} ) \\{\frac{\partial^{2}G}{\partial\alpha^{2}} \leq 0} & (3.2)\end{matrix}$are fulfilled for both functions G⁻(α) and G₊(α). Thereby it is ensuredthat for each intermediate state G(α) the conditions according tocertain embodiments of the invention are satisfied as well, and thecrack remains within the cleavage plane during the complete dividingprocess.

FIG. 13 shows an example of a balanced situation. When complying withthe condition according to certain embodiments of the invention for bothfunctions G⁻(α) and G₊(α) the function g has its maximum also in anypossible (not known) intermediate states during the separation processat α=0, and a self-adjustment of the crack within the cleavage plane isensured for the complete separation process between the start and targetposition. A deflection of the crack as shown in FIG. 7 is impeded andthe crack tip moves in any time step t=t₀+dt of the separation processin the cleavage direction α=0 as shown in FIG. 14.

The calculation of the functions G⁻(α) and G₊(α) and the balancing ofthe stress fields can also be carried out iteratively as well as for allpossible combinations of known maximum errors due to pre-adjustment. Thecontrol and dimensioning of the stress fields is in simple fashionpossible for example by control of the laser power and/or the variationof laser focus and/or the arrangement of cooling nozzles relative to thelaser spot using the known methods. Nevertheless, further alternativesmay equally be considered.

The invention can further be carried such that during the step oftesting the conditions (2.1) or (2.2) a maximum admissible range ofangles α₁<α<α₂ is determined. In this range

$\frac{\partial^{2}G}{\partial\alpha^{2}} \leq 0$must be valid for condition (2.1), or G(α)≧2γ_(e)(α) must be valid forcondition (2.2), respectively. The determined angular range is thencompared with a predetermined mean alignment- or adjustment-error of anorientation of the crystallographic (2′) relative to the separationdevice. The control of the stress fields (3′, 4′) and/or the adaption ofthe pre-adjustment of the crystal is then carried out in dependence ofthe result of the comparison.

The invention is not limited to the separation of GaAs-wafers, which aredescribed herein as an embodiment. Rather, the invention may also beapplied to any single crystal. Approximated values for a CaF₂(111)-plane are for example

γ_(s)≈0.47 J/m² (ab initio Hartree-Fock calculation) and

β_(e)≈(3.31−6.8)×10⁻¹⁰ J/m and with h=0.32 nm:

β_(e)/h≈(1.03−2.13) J/m².

Further, the invention is also applicable to single crystals, which areformed as single crystalline layers on a single crystalline substrate.The layer and the substrate can thereby be formed from the same or adifferent material composition.

In the above embodiments, a specific arrangement of the stress fieldshas been described. Therein, the propagation of the crack is maintainedwithin a stress filed between the temperature sink and the temperaturesource. The invention is, however, not restricted to that specificarrangement. For example, the stress fields can also be provided by themere presence of a temperature sink or alternatively of a temperaturesource, and/or the propagation front is maintained in front of the sinkand/or source and not behind one of them or between both.

The invention can further be embodied as a computer program product,which is arranged to perform and control the steps provided in theappended method claims.

1. A method of separating single crystals, particularly of plates,wafers or parts thereof, comprising: pre-adjusting a crystallographiccleavage plane relative to a cleavage device; determining a stressintensity using at least one stress field; for the at least one stressfield, determining an energy release rate G(α) dependent on a possibledeflection angle from the cleavage plane upon crack propagation in asingle crystal; generating the at least one stress field, whereinG(0)≧2γ_(e)(0) and simultaneously at least one of the followingconditions is satisfied: $\begin{matrix}{{{\frac{\partial G}{\partial\alpha}}_{\alpha = 0} \leq {2\frac{\beta_{e}}{h}\mspace{14mu}{if}\mspace{14mu}\frac{\partial^{2}G}{\partial\alpha^{2}}} \leq 0}{or}} & (2.1) \\{{{\frac{\partial G}{\partial\alpha}} \leq {2\frac{\beta_{e}}{h}{\forall{{\alpha\text{:}\alpha_{1}} < \alpha < \alpha_{2}}}}},} & (2.2)\end{matrix}$ wherein: α denotes the possible deflection angle from thecleavage plane upon crack propagation, α₁, α₂ denotes a range of angles,in which the necessary condition for a crack propagation G(α)≧2γ_(e)(α)is satisfied, G(α) denotes the mechanical-energy-release rate dependenton a deflection of the crack from the cleavage plane about angle α,γ_(e)(0) denotes an effective surface energy of cleavage surface, γ_(e)denotes an effective surface energy which depends from the direction,β_(e) denotes an effective step energy (material specific), and hdenotes a step height (material specific).
 2. The method according toclaim 1, wherein the step of controlling or regulating the stress fieldsincludes the following steps: verifying the validity of G(0)≧2γ_(e)(0)and the at least one of the conditions (2.1) or (2.2) for the energyrelease rate G(α) obtained for the given stress fields dependent onpossible deflection angles (α); dependent on the result of theverification, adjusting the stress fields or the pre-adjustment of thecleavage plane relative to the cleavage device.
 3. The method accordingto claim 1, wherein the step of determining the energy release rate G(α)for the adjusted stress fields or the adapted pre-adjustment as well asthe following step of the verification are repeated, if at leastG(0)≧2γ_(e)(0) or the at least one of the conditions (2.1) or (2.2) isnot fulfilled; and the stress fields or the pre-adjustment are adjustedin response thereto.
 4. The method according to claim 1, wherein aninitial crack is generated as a continuous edge-crack directed along thecleavage plane.
 5. The method according to claim 1, wherein the stressintensity (K) is generated thermally or mechanically.
 6. The methodaccording to claim 1, wherein, in advance: the energy release rate (G)is determined depending on the angle (α) via simulation calculations;and/or the material specific step energy (β_(e)) and the materialspecific step height (h) are determined and preset; or the directiondependent effective surface energy (γ_(e)) is determined and preset. 7.The method according to claim 1, wherein a simulation or calculation ofthe stress fields is performed in advance for at least one of a numberof positions of the crack along its propagation path across the singlecrystal prior to generating at least one of the stress fields.
 8. Themethod according to claim 1, wherein the stress fields in the vicinityof a tip of the crack are measured during the propagation of the crack;and the measured stress fields are thereafter preset for the step ofdetermining the energy release rate G(α) dependent on possible angulardeflections (α).
 9. The method according to claim 1, wherein the stressfields are measured during the propagation of the crack for verifyingthe conditions, G(0)≧2γ_(e)(0), and at least one of (2.1) or (2.2) andare regulated according to a recipe in order to align the same, thusforming a closed loop control.
 10. The method according to claim 1,wherein the energy release rate G⁻(α) is calculated for the case of aninfinitesimal propagation in a start region of the crack dependent onpossible deflections about the angle (α), the energy release rate G₊(α)is calculated for a planned target region under the assumption that thecrack has remained within the cleavage plane, and the stress intensityis adjusted such that conditions (2.1) and (2.2) are fulfilled for bothfunctions G⁻(α) and G₊(α).
 11. A method according to claim 1, wherein asingle crystal from a group comprising a II-VI or III-V semiconductorcompound, comprising a single crystal comprising GaAs, GaP or InP, or aSi single crystal, or a CaF single crystal, or a SiC— or sapphire singlecrystal or a GaN single crystal, or a single crystalline plate of thesetypes is separated.
 12. A method according to claim 1, wherein a maximumvalue for a possible adjustment error of an orientation of thecrystallographic cleavage plane relative to a cleavage device isprovided, and the step of controlling or regulating the at least one ofthe stress fields or adapting the pre-adjustment includes a comparisonof the at least one condition (2.1) or (2.2) to be maintained duringpropagation with an angular range represented by the maximum possibleadjustment error, wherein the control of the stress fields or theadaption of the pre-adjustment is performed dependent on the result ofthe comparison.
 13. The method of claim 1, wherein the step ofgenerating the at least one stress field comprises controlling orregulating the at least one stress field or the pre-adjustment such thatthe crack further propagates in the single crystal, and such thatG(0)≧2γ_(e)(0) and such that at least one of condition 2.1 or condition2.2 is satisfied.
 14. The method of claim 1, wherein the step ofgenerating the at least one stress field comprises adjusting thecrystallographic cleavage plane relative to the cleavage device.